EUROPEAN ORGANISATION FOR NUCLEAR RESEARCH (CERN)
Eur. Phys. J. C 80 (2020) 737
DOI:10.1140/epjc/s10052-020-8102-8
CERN-EP-2020-044 27th August 2020
Search for a scalar partner of the top quark in the
all-hadronic t ¯t plus missing transverse momentum
final state at
√
s
= 13 TeV with the ATLAS detector
The ATLAS Collaboration
A search for direct pair production of scalar partners of the top quark (top squarks or scalar third-generation up-type leptoquarks) in the all-hadronic t ¯t plus missing transverse momentum
final state is presented. The analysis of 139 fb−1of
√
s= 13 TeV proton–proton collision
data collected using the ATLAS detector at the LHC yields no significant excess over the Standard Model background expectation. To interpret the results, a supersymmetric model is used where the top squark decays via ˜t → t(∗)χ˜10, with t(∗)denoting an on-shell (off-shell) top quark and ˜χ10the lightest neutralino. Three specific event selections are optimised for the following scenarios. In the scenario where mt˜> mt + mχ˜0
1, top squark masses are excluded
in the range 400–1250 GeV for ˜χ10masses below 200 GeV at 95% confidence level. In the
situation where mt˜∼ mt+ mχ˜0
1, top squark masses in the range 300–630 GeV are excluded,
while in the case where mt˜ < mW + mb+ mχ˜0
1 (with mt˜ − m
˜ χ0
1 ≥ 5 GeV), considered for the
first time in an ATLAS all-hadronic search, top squark masses in the range 300–660 GeV are excluded. Limits are also set for scalar third-generation up-type leptoquarks, excluding leptoquarks with masses below 1240 GeV when considering only leptoquark decays into a top quark and a neutrino.
© 2020 CERN for the benefit of the ATLAS Collaboration.
Reproduction of this article or parts of it is allowed as specified in the CC-BY-4.0 license.
1 Introduction
Supersymmetry (SUSY) [1–6] is an extension of the Standard Model (SM) that can resolve the gauge
hierarchy problem [7–10] by introducing supersymmetric partners of the SM bosons and fermions. The
SUSY partner to the top quark, the top squark, plays an important role in cancelling out potentially large
top-quark loop corrections to the Higgs boson mass [11, 12]. Naturalness arguments suggest that the
superpartners of the third-generation quarks may be O( TeV), and thus experimentally accessible at the
Large Hadron Collider (LHC) [13,14]. The superpartners of the left- and right-handed top quarks, ˜tLand
˜tR, mix to form two mass eigenstates, ˜t1 and ˜t2, where ˜t1is the lighter one. Throughout this paper, it is
assumed that ˜t2has sufficiently high mass such that the analysis is sensitive to ˜t1only, which is labelled ˜t in
the following.
R-parity-conserving SUSY models [15] may also provide a dark-matter candidate through the lightest
supersymmetric particle (LSP), which is stable [16,17]. In these models, the supersymmetric partners
are produced in pairs. At the LHC, top squarks are produced mostly via gluon–gluon fusion as well as quark–antiquark annihilation. In a simplified scenario where the first- and second-generation squarks and gluinos are decoupled, the cross section of direct top squark pair production is largely decoupled from the specific choice of SUSY model parameters except for the top squark mass. This production cross
section falls steeply with increasing top squark mass, ranging from 10.0 ± 6.7 pb for mt˜ = 300 GeV to
0.89 ± 0.13 fb for mt˜= 1300 GeV [18–21].
In this paper, each top squark is assumed to decay into a top quark (that may be either on-shell or off-shell) and the LSP, which is assumed to be the lightest neutral mass eigenstate of the partners of the electroweak
gauge and Higgs bosons, i.e. the lightest neutralino, ˜χ10. The degree to which the top quark is off-shell
is directly related to the mass difference between ˜t and ˜χ10. The top squark decay scenarios considered
are shown in Figures 1(a)–1(c): the top quark is on-shell in two-body decays (˜t → t ˜χ10), three-body
decays contain an off-shell top quark but the W boson is on-shell (˜t → t∗χ˜10 → bW ˜χ 0
1), and in four-body
decays both the top quark and W boson are off-shell (˜t → t∗χ˜10 → bW ∗χ˜0 1 → b f f 0χ˜0 1, where f and f 0 are fermions originating from the off-shell W boson decay). Only hadronic W boson decays are considered in the following.
This paper presents a search for top squark pair production with an experimental signature of at least two
jets, large missing transverse momentum, and no electrons or muons, using 139 fb−1of proton–proton
(pp) collision data provided by the LHC at a centre-of-mass energy of √
s= 13 TeV and collected by the
ATLAS detector in 2015–2018. Previous searches have been performed by both the ATLAS [22–28] and
CMS [29–37] collaborations. In this search, enhanced sensitivity to two-body top squark decays, where
m˜t− m
˜ χ0
1is greater than the top quark mass, mt, is achieved by the analysis of the full LHC Run 2 dataset and the exploitation of techniques designed to efficiently reconstruct top quarks that are Lorentz-boosted in the
laboratory frame. Sensitivity to compressed scenarios, where m˜t− mχ˜0
1
∼ mt, is extended compared with
previous searches through the analysis of events in which high-transverse-momentum jets from initial-state radiation (ISR) boost the top squark system in the transverse plane. Finally, sensitivity to the four-body decay scenario where mt˜− mχ˜0
1 is less than the sum of the W boson mass, mW, and the b-quark mass,
mb, is achieved by extending the identification efficiency for low-transverse-momentum b-hadron decays
through the use of charged-particle tracking information, adding sensitivity to the all-hadronic channel in comparison with previous searches. All sensitivities are also increased thanks to global enhancements in detector performance achieved by the end of LHC Run 2, including more precise estimates of the statistical
˜ t ˜ t t W t W p p ˜ χ01 b q q ˜ χ01 b q q (a) ˜ t ˜ t W W p p ˜ χ01 b q q ˜ χ01 b q q (b) ˜ t ˜ t p p b q q ˜ χ01 b q q ˜ χ01 (c) LQu3 LQu3 p p ν, τ t, b ν, τ t, b (d)
Figure 1: Decay topologies of the signal models considered in the analysis: (a) two-body, (b) three-body, (c) four-body top squark decays, the top quarks being produced in pairs, and (d) up-type, third-generation scalar leptoquark pair production, with both leptoquarks decaying into a top quark and a neutralino or a bottom quark and a τ-lepton. For simplicity, no distinction is made between particles and antiparticles. Only hadronic W boson decays are shown.
significance of missing transverse momentum in an event [38] and improved identification efficiencies for
jets containing b-hadrons [39]. The interpretation of the results uses simplified models [40–42].
As has been demonstrated previously [23–25,43,44], top squark searches are sensitive to a variety of
additional signal models such as top squarks originating from gluino decays [40–42], top squark decays
via charged electroweak SUSY partners [40–42], mediator-based dark-matter models [45–50], scalar
dark-energy models [51], and third-generation scalar leptoquarks [52–58]. In this paper, the results are
interpreted in models considering the pair production of up-type, third-generation scalar leptoquarks (LQu3),
as shown in Figure1(d), assuming that the LQu3 only interact with leptons and quarks from the same
generation [59]. Similar LQu3interpretations have been performed by both the ATLAS [44] and CMS [60]
collaborations. The third-generation leptoquark production cross section is identical to that of top squark
production and the LQu3→ tν decay channel has the same experimental signature as heavy top squarks
decaying into massless neutralinos, and thus additional sensitivity is achieved compared with previous LQu3results.
2 ATLAS detector
The ATLAS experiment [61–63] at the LHC is a multipurpose particle detector with a cylindrical forward–
backward- and φ-symmetric geometry and an approximate 4π coverage in solid angle.1 It consists of an
inner tracking detector surrounded by a thin superconducting solenoid providing a 2 T axial magnetic field, electromagnetic and hadron calorimeters, and a muon spectrometer. The inner tracking detector covers the pseudorapidity range |η| < 2.5. It consists of silicon pixel, silicon microstrip, and transition radiation tracking detectors. Lead/liquid-argon (LAr) sampling calorimeters provide electromagnetic (EM) energy measurements with high granularity. Hadronic calorimetry is provided by a steel/scintillator-tile calorimeter covering the central pseudorapidity range (|η| < 1.7). The endcap and forward regions are instrumented with LAr calorimeters for both the EM and hadronic energy measurements up to |η| = 4.9. The muon spectrometer surrounds the calorimeters and features three large air-core toroidal superconducting magnets with eight coils each, providing coverage up to |η| = 2.7, as well as a system of precision tracking chambers and fast detectors for triggering. The field integral of the toroids ranges between 2 and 6 T·m across most of the detector.
3 Data collection and simulated event samples
The data were collected from 2015 to 2018 at a pp centre-of-mass energy of 13 TeV with 25 ns bunch
spacing, resulting in a time-integrated luminosity of 139.0 ± 2.4 fb−1[64], measured using the LUCID-2
detector [65]. Multiple pp interactions occur per bunch crossing (pile-up) and the average number of these
interactions in the data was measured to be hµi = 34. A two-level trigger system [66] is used to select
events. The first-level trigger is implemented in hardware and uses a subset of the detector information to reduce the event rate to at most 100 kHz. This is followed by a software-based trigger that reduces the accepted event rate to 1 kHz (on average) for offline storage.
Selected events are required to pass a missing transverse momentum (whose magnitude is denoted by ETmiss)
trigger [67], which is fully efficient for events with reconstructed ETmiss> 250 GeV (the ETmissreconstruction
is described in Section4). In order to estimate the background originating from SM processes, events are
also selected at lower values of ETmissusing single-electron, single-muon, and single-jet triggers. Electron
and muon triggers yield an approximately constant efficiency in the presence of a single isolated electron
or muon with transverse momentum (pT) above 27 GeV (see Section4for details of the electron, muon,
and jet reconstruction); these triggers are needed for the estimation of Z → ν ¯ν production in association
with heavy-flavour jets (Z + jets) and top pair production in association with Z → ν ¯ν (t¯t+ Z) backgrounds.
Triggers based on the presence of a single jet were used to collect data samples for the estimation of the
multijet and all-hadronic t ¯t backgrounds. The jet pTthresholds after energy calibration ranged from 50 to
400 GeV. In order to stay within the bandwidth limits of the trigger system, only a fraction of the events passing the jet triggers were recorded to permanent storage.
Monte Carlo (MC) simulations are used to model the SUSY and leptoquark signals, as well as to
aid in the description of the background processes. SUSY signal models were all generated with
MadGraph5_aMC@NLO 2.6.2 [68] at leading order (LO) in QCD, while leptoquark signals were
1 ATLAS uses a right-handed coordinate system with its origin at the nominal interaction point (IP) in the centre of the detector
and the z-axis along the beam pipe. The x-axis points from the IP to the centre of the LHC ring, and the y-axis points upwards. Cylindrical coordinates (r, φ) are used in the transverse plane, φ being the azimuthal angle around the z-axis. The pseudorapidity is defined in terms of the polar angle θ as η = − ln tan(θ/2). Angular distance is measured in units of ∆R ≡
p
generated with MadGraph5_aMC@NLO 2.4.3 at next-to-leading order (NLO) in QCD. All signal samples
were interfaced to Pythia 8.230 [69] for the parton showering (PS) and hadronisation, and with EvtGen
1.6.0 [70] for the b- and c-hadron decays.
The parton distribution function (PDF) set used for the generation of the signal samples is NNPDF2.3
LO [71] for SUSY signals and NNPDF3.0 NLO [72] for leptoquark signals, with the A14 [73] set of tuned
underlying-event and parton shower parameters (UE tune). Matching of the matrix element (ME) with
parton showering was performed following the CKKW-L prescription [74], with a matching scale set to one
quarter of the mass of the top squark or leptoquark. All signal cross sections are calculated to approximate next-to-next-to-leading order (NNLO) in the strong coupling constant, adding the resummation of soft
gluon emission at next-to-next-to-leading-logarithm accuracy (approximate NNLO+NNLL) [18,19,75,
76].
The top squark mixing parameter between ˜tLand ˜tRwas set to be maximal.2 Finally, the top quark mass
was set to 172.5 GeV in all simulated samples.
SM background samples were generated with different MC event generators depending on the process.
Details of the generators and parton showering used for the different processes are shown in Table1.
Table 1: Overview of the simulated background samples.
Process ME event generator PDF PS and UE tune Cross-section hadronisation calculation V +jets (V = W/Z) Sherpa 2.2.1 [78] NNPDF3.0 NNLO Sherpa Default NNLO [79] t ¯t+ V aMC@NLO 2.3.3 NNPDF3.0 NLO Pythia 8.210 A14 NLO [68]
t ¯t Powheg-Box v2 [80] NNPDF3.0 NNLO Pythia 8.230 A14 NNLO+NNLL [81–86] Single top Powheg-Box v2 NNPDF3.0 NNLO Pythia 8.230 A14 NNLO+NNLL [87–89] Diboson Sherpa 2.2.1-2.2.2 NNPDF3.0 NNLO Sherpa Default NLO
t ¯tH aMC@NLO 2.2.3 NNPDF3.0 NLO Pythia 8.230 A14 NLO [90–93] tW Z, t Z aMC@NLO 2.3.3 NNPDF3.0 NLO Pythia 8.212,8.230 A14 NLO
The detector simulation [94] was performed using either Geant4 [95] or a fast simulation framework,
where the showers in the electromagnetic and hadronic calorimeters are simulated with a parameterised
description [96] and the rest of the detector is simulated with Geant4. All signal samples were produced
using the fast simulation, while SM background samples used the Geant4 set-up. All MC samples were produced with a varying number of simulated minimum-bias interactions overlaid on the hard-scattering
event, to account for pile-up. These interactions were produced using Pythia 8.2 with the A3 tune [97] and
NNPDF2.3 LO PDF set. The simulated events are reweighted to match the distribution of the number of pp interactions per bunch crossing in data. Corrections are applied to the simulated events to account for differences between data and simulation for the lepton trigger, reconstruction, identification and isolation efficiencies, and for the lepton and jet momentum scale and energy resolution. Corrections are also applied to the efficiency of identifying jets containing b-hadrons (b-jets), the probability of mis-tagging jets containing only charm hadrons (c-jets) and only lighter hadrons (light-flavour jets), and the probability of mis-tagging jets originating from the hard pp scattering as pile-up jets.
2This refers to the Higgs–top-squark trilinear mixing term; the scenario of maximal mixing allows the top squark masses to be as
4 Event reconstruction
Events are required to have a primary vertex [98,99] reconstructed from at least two tracks [100] with
pT> 500 MeV. Among the vertices found, the vertex with the largest summed p2
Tof the associated tracks
is designated as the primary vertex.
Calorimeter jets are built from topological clusters of energy in the calorimeter [101], calibrated to the
electromagnetic scale, using the anti-kt algorithm with radius parameter R = 0.4 [102, 103]. These
types of jets are referred to as ‘jets’. Jet transverse momenta are further corrected to the corresponding
particle-level jet pT, based on the simulation [104]. Remaining differences between data and simulated
events are evaluated and corrected for using in situ techniques, which exploit the transverse momentum balance between a jet and a reference object such as a photon, Z boson, or multijet system in data. After these calibrations, all jets in the event with pT > 20 GeV and |η| < 4.5 must satisfy a set of loose jet-quality
requirements [105]. In the four-body analysis, the leading jet in pTmust satisfy a set of tighter jet-quality
requirements. These requirements are designed to reject jets originating from sporadic bursts of detector noise, large coherent noise or isolated pathological cells in the calorimeter system, hardware issues,
beam-induced background or cosmic-ray muons [105]. If these jet requirements are not met, the event is
discarded. All jets are required to have pT > 20 GeV and |η| < 2.8 to be considered in this analysis. In
addition, the ‘medium’ working point of the track-based jet vertex tagger [106,107] is required for jets
with pT < 120 GeV and |η| < 2.5, to reject jets that originate from pile-up interactions.
Jets which contain b-hadrons and are within the inner-detector acceptance (|η| < 2.5) are identified as
‘b-tagged’ using a multivariate algorithm that exploits the impact parameters3of the charged-particle tracks,
the presence of secondary vertices, and the reconstructed flight paths of b- and c-hadrons inside the jet [39]. The output of the multivariate algorithm is a single b-tagging output score, which signifies the likelihood of a jet to contain b-hadrons. The average identification efficiency of jets containing b-hadrons is 77% as determined in simulated t ¯t events. Using the same simulated sample, a rejection factor of approximately 110 (5) is reached for jets initiated by light quarks and gluons (charm quarks).
In order to identify low-pT b-hadrons that are not contained in jets passing the pT > 20 GeV requirement,
‘track-jets’ are reconstructed from inner-detector tracks using the anti-kt algorithm with radius parameter
R= 0.4. Tracks considered for inclusion in track-jets are required to have pT > 500 MeV, |η| < 2.5, at
least seven hits in the silicon microstrip and pixel detectors, no more than one hit shared by multiple tracks in the pixel detector, no more than one missing hit in the pixel detector, and no more than two missing hits in the silicon microstrip detector. Additional requirements on the longitudinal impact parameter
projected along the beam direction (|z0sin(θ)| < 3 mm) reduce the pile-up contributions and improve the
efficiency in selecting tracks from the hard-scatter vertex. Track-jets are required to have pT> 5 GeV, more
than one track within the jet radius, |η| < 2.5, and not overlap with the leading non-b-tagged jet in the
event (∆R > 0.4). The standard b-tagging algorithm is employed for track-jets [108] and the selection
requirement is tighter than for regular jets, due to the larger amount of background at low pT. The average
identification efficiency for jets containing b-hadrons is 70% as determined in simulated t ¯t events. Using the same simulated sample, a rejection factor of approximately 200 (10) is reached for jets initiated by light quarks and gluons (charm quarks).
3The transverse impact parameter, d
0, is defined as the distance of closest approach of a track to the beam-line, measured in the
transverse plane. The longitudinal impact parameter, z0, corresponds to the z-coordinate distance between the point along the
Electron candidates are reconstructed from clusters of energy deposits in the electromagnetic calorimeter that are matched to a track in the inner detector. They are required to have |η| < 2.47 and pT > 4.5 GeV, and
must pass a loose likelihood-based selection [109,110]. The impact parameter along the beam direction is
required to be less than 0.5 mm. The electromagnetic shower of an electron can also be reconstructed as a
jet such that a procedure is required to resolve this ambiguity. In the case where the separation4between an
electron candidate and a non-b-tagged (b-tagged) jet is ∆Ry < 0.2, the candidate is considered to be an
electron (b-tagged jet). This procedure uses a b-tagged jet definition that is looser than the one described earlier, to avoid selecting electrons from heavy-flavour hadron decays. If the separation between an electron candidate and any jet satisfies 0.2 < ∆Ry < 0.4, the candidate is considered to be a jet, and the electron
candidate is removed.
Muons are reconstructed by matching tracks in the inner detector to tracks in the muon spectrometer and
are required to have |η| < 2.7 and pT > 4 GeV [111]. The impact parameter along the beam direction
is required to be less than 0.5 mm. Events containing muons identified as originating from cosmic rays,
|d0| > 0.2 mm and |z0| > 1 mm, or as poorly reconstructed, σ(q/p)/|(q/p)| > 0.2, are removed. Here,
σ(q/p)/|(q/p)| is a measure of the momentum uncertainty for a particle with charge q. Muons are discarded if they are within ∆R = 0.4 of jets that survive the electron–jet overlap removal, except when the number of tracks associated with the jet is less than three, where the muon is kept and the jet discarded. The requirements on electrons and muons are tightened for the selection of events in background control
regions (described in Section6) containing at least one electron or muon. The electrons and muons
passing the tight selection are called ‘control’ electrons or muons in the following, as opposed to ‘baseline’ electrons and muons, which are only required to pass the requirements described above. Control electrons
and muons are required to satisfy the ‘FCLoose’ pT-dependent track-based and calorimeter-based isolation
criteria [112]. The calorimeter-based isolation is determined by taking the ratio of the sum of energy
deposits in a cone of ∆R = 0.2 around the electron or muon candidate to the sum of energy deposits associated with the electron or muon. The track-based isolation is estimated in a similar way but using a variable cone size with a maximum value of ∆R = 0.2 for electrons and ∆R = 0.3 for muons. Electron candidates are required to pass a ‘tight’ likelihood-based selection. The impact parameter of the electron in the transverse plane is required to be less than five times the transverse impact parameter uncertainty (σd0). Further selection criteria are also imposed on reconstructed muons: muon candidates are required to pass a ‘medium’ quality selection and meet the |d0| < 3σd0requirement.
The pmissT vector is the negative vector sum of the pTof all selected and calibrated electrons, muons, and
jets in the event, plus an extra term (‘soft’ term) added to account for energy depositions in the event that are not associated with any of the objects. The ‘soft’ term is calculated from inner-detector tracks
(pT > 500 MeV and matched to the primary vertex, to make it resilient to pile-up contamination) not
associated with selected objects [113,114]. The missing transverse momentum calculated using only the
tracking system (denoted by pmiss,trackT , with magnitude ETmiss,track) is computed from the vector sum of
the inner-detector tracks with pT > 500 MeV and |η| < 2.5 that are associated with the event’s primary
vertex.
Hadronically decaying τ-lepton candidates are identified as non-b-tagged jets with |η| < 2.5 and a maximum of four inner-detector tracks matched to them. They are only used in some regions to veto events with τ-lepton candidates most likely originating from W → τν decays, which are identified with the additional
requirement that the ∆φ between the τ-lepton candidate and the pmissT is less than π/5.
4For the overlap removal, rapidity (y) is used instead of pseudorapidity: y = 1 2ln
E+pz
E−pz, where E is the energy and pzis the
z-component of the momentum of the object. The separation is then defined as ∆Ry≡
p
5 Signal region definitions
The experimental signature of this search, for all signal topologies, consists of multiple jets, one or two of
which are b-tagged, no electrons and muons (following the baseline definition described in Section4), and
large missing transverse momentum. The ETmisstrigger is used to collect the data in all signal regions.
Beyond these common requirements, four sets of signal regions (SRA–D) are defined to target each decay
topology and kinematic regime, as shown in Figure2. SRA (SRB) is sensitive to the production of
high-mass ˜t pairs that each undergo a two-body decay with large (medium) ∆m(˜t, ˜χ10), or the production
of high-mass leptoquark pairs. Both SRA and SRB employ top-quark mass-reconstruction techniques to reject background, of which the dominant source is associated production of a Z boson with heavy-flavour jets, with the Z decaying into neutrinos (Z + jets). SRC targets compressed two/three-body top squark
decays with ∆m(˜t, ˜χ10) ∼ mtand has t ¯t production as the dominant background contribution. A common
preselection is defined for SRA–C: at least four jets are required (Nj ≥ 4), at least two of which must be
b-tagged (Nb ≥ 2), and the leading four jets must satisfy pT > 80, 80, 40, 40 GeV. SRD targets highly
compressed four-body top squark decays and uses track-jets to identify b-hadrons with low pT. As in SRA
and SRB, the dominant source of background in SRD is Z + jets. In both SRC and SRD, a high-pT jet
originating from ISR is used to improve sensitivity to the targeted decays.
200
200
) [GeV]
t
~
m(
) [GeV]
0χ∼
1m
(
t ) = m 0 1 χ∼ , t ~ m( Δ W + m b ) = 0 0 1 χ∼ , t ~ m( Δ0
4-bo
dy d
ecays
3-bo
dy d
ecays
2-body decays
m
<
m
∼
χ
0 1t
∼
) = m 0 1 χ∼ , t ~ m( ΔSRB
SRA
SR
C
SRD
Figure 2: Schematic representation of the various topologies targeted by the different signal regions defined in the analysis (SRA, SRB, SRC, SRD). SRA and SRB are orthogonal and the exact requirements made in the signal regions are detailed in the text and Table2.
5.1 Signal regions A and B
SRA is optimised for exclusion at 95% confidence level (CL) of the scenario where mt˜= 1300 GeV and
m
˜ χ0
1 = 1 GeV, while SRB is optimised for mt˜= 700 GeV and mχ˜
0
1 = 400 GeV. SRA and SRB have the best
sensitivity to up-type, third-generation scalar leptoquarks, when leptoquarks decay via LQu3 → tν.
To avoid a loss of efficiency when the top quark has pT > 200 GeV and its daughters are close to each
other, the two hadronic top candidates are reconstructed by using the anti-kt algorithm to cluster R = 0.4
jets, using radius parameters of R = 0.8 and R = 1.2, similar to the technique used in the previous ATLAS
search [23]. Each reclustered jet is assigned a mass which is computed from the four-momenta of its
jet constituents. Two R = 1.2 reclustered jets, representing top candidates, are required, and the leading
reclustered R = 1.2 jet must have a mass (m1R=1.2) greater than 120 GeV. To optimise signal efficiency
regardless of the subleading top candidate reconstruction success (measured by how close the candidate mass is to the top quark mass), the events are divided into three categories based on the subleading
R = 1.2 reclustered jet mass (mR=1.2
2 ): the ‘TT’ category includes events with m
R=1.2
2 > 120 GeV,
corresponding to successfully reconstructing a subleading top candidate; the ‘TW’ category contains events
with 60 < m2R=1.2 < 120 GeV, corresponding to successfully reconstructing a subleading W candidate; and
the ‘T0’ category represents events with m2R=1.2 < 60 GeV, corresponding to not reconstructing a top nor a W candidate.
In SRA, in addition to using the mass of the reclustered jets, information about the flavour content of the reclustered jet is used to improve background rejection. For all SRA categories, a b-tagged jet is required
to be within ∆R = 1.2 of the leading reclustered R = 1.2 jet, j1R=1.2(b), while in the SRA-TT category,
the same selection is made for the subleading R = 1.2 jet, j2R=1.2(b). A requirement is also made on the
leading R = 0.8 reclustered jet mass (mR1=0.8 > 60 GeV) in SRA.
In order to reject events with mismeasured ETmissoriginating from multijet and hadronic t ¯t decays, the
minimum difference in azimuthal angle between the pmissT and the leading four jets (
∆φmin pT,1−4, pmiss T
) is required to be greater than 0.4.
The most powerful rejection of background comes from requiring that the object-based ETmisssignificance
(S) [38] is greater than 25 (14) in SRA (SRB). This variable characterises the ETmissaccording to the pT,
pTresolution, and φ resolution of all objects in the event, and is defined as:
S= E miss T q σ2 L(1 − ρ 2 LT) ,
where σLis the expected resolution of the total longitudinal momentum (relative to the direction of pmissT )
of all objects in the event as a function of the pT of each object. Likewise, ρLTis the correlation factor
between the longitudinal and transverse momentum resolutions for all objects.
Substantial t ¯t background rejection is provided by additional requirements to reject events in which one W
boson decays via a lepton plus neutrino. The first requirement is that the transverse mass (mT) calculated
from the ETmissand the b-tagged jet closest in φ to the pmissT direction and defined as:
mb,min
T =
q
must be above 200 GeV. The second requirement consists of vetoing events containing hadronic τ-lepton candidates likely to have originated from a W → τν decay (τ-veto).
To reject events that contain b-tagged jets from gluon splitting, requirements are made on the angular distance
between the two leading b-tagged jets, ∆R (b1, b2). In SRB, an additional requirement of m
b,max
T > 200 GeV
is made, where mTb,maxis analogous to mTb,minexcept that the transverse mass is computed with the b-tagged
jet that has the largest ∆φ relative to the pmissT direction. This requirement is a more stringent version of
mb,min
T , requiring that the leading two b-tagged jets are not near the p
miss T .
Finally, to allow the statistical combination of SRA and SRB, SRA is required to have the mT2, χ2variable
greater than 450 GeV, while SRB is required to have mT2, χ2 < 450 GeV. The mT2, χ2 variable is based
on mT2 [115, 116] and is constructed from the direction and magnitude of pmissT and the direction of
each of the top candidates, reconstructed using a χ2-like method with R = 0.4 jets as inputs. The
minimisation for finding the top candidates used in mT2, χ2 is performed in terms of a χ2-like penalty
function, χ2= (mcand− mtrue)2/mtrue, where mcandis the top quark or W boson candidate mass and mtrueis
set to 80.4 GeV for W boson candidates and 173.2 GeV for top quark candidates.5 Initially, single or pairs
of R = 0.4 jets, whichever configuration results in a mass closest to mW, form W boson candidates, which
are then combined with additional b-jets in the event to construct top quark candidates. When calculating mT2, χ2the momenta of top quark candidates selected by the χ2method are used, while the masses of the
top quarks are set to 173.2 GeV and the invisible particles are assumed to be massless. Table2summarises
all the selection criteria used in SRA and SRB.
In addition to SRA and SRB, which are optimised for high m˜tvia a statistical combination, a signal region
is optimised for discovery. This region, SRA-TT-Disc, has the same requirements as SRA-TT, with the exception of a less stringent requirement of S > 11. When setting exclusion limits on specific signal models, SRA-TT-Disc is not considered.
5These mass values were the world averages of the W boson and top quark masses at the time of the development of this method
which was for the last iteration of this search [23]. Updated measurements of the masses of the W boson and top quark have a negligible effect on this method and thus were not included.
Table 2: Selection criteria for SRA and SRB. Each signal region is separated into three categories based on reconstructed top candidate masses. A dash indicates that no selection is applied.
Variable/SR SRA-TT SRA-TW SRA-T0 SRB-TT SRB-TW SRB-T0
Trigger ETmiss Emiss T > 250 GeV N` exactly 0 Nj ≥ 4 pT,2 > 80 GeV pT,4 > 40 GeV ∆φmin pT,1−4, pmiss T > 0.4 Nb ≥ 2 mb,min T > 200 GeV τ-veto X mR=1.2 1 > 120 GeV mR=1.2
2 > 120 GeV 60–120 GeV < 60 GeV > 120 GeV 60–120 GeV < 60 GeV
mR=0.8 1 > 60 GeV – jR=1.2 1 (b) X – j2R=1.2(b) X – ∆R (b1, b2) > 1.0 – > 1.4 mb,max T – > 200 GeV S > 25 > 14 mT2, χ2 > 450 GeV < 450 GeV 5.2 Signal regions C
SRC is optimised for the case where ∆m(˜t, ˜χ10) ∼ mt, a regime in which the signal topology is similar to
SM t ¯t production. In the presence of high-momentum ISR jets, the di-top-squark system is boosted in the transverse plane and better discrimination can be achieved. A recursive jigsaw reconstruction technique,
as described in Ref. [117], is used to divide each event into an ISR hemisphere (denoted by ‘ISR’) and a
sparticle hemisphere (denoted by ‘S’), where the latter consists of the pair of candidate top squarks. Objects are grouped together according to their proximity in the laboratory frame’s transverse plane by minimising the reconstructed transverse masses of the ISR system and sparticle system, simultaneously over all choices of object assignment. Kinematic variables are then defined, based on this assignment of objects to either the ISR system or the sparticle system.
The ratio of the ETmissto the pTof the ISR system (pISRT ), defined as RISR, is proportional to the ratio of the ˜ χ0 1 and ˜t masses [118,119]: RISR≡ E miss T pISR T ∼ m ˜ χ0 1 mt˜ .
Due to the scaling of RISRwith the ratio of mχ˜0
1 to mt˜, signals with ∆m(˜t, ˜ χ0
1) ∼ mtare expected to form
a peak in the RISRdistribution, with the location of the peak depending on mχ˜0
1 divided by mt˜. In order
to maximise the sensitivity for a wide range of mχ˜0
1 to mt˜ratio values, the events are divided into five
categories, defined by non-overlapping ranges of RISRand targeting different top squark and ˜χ
0
1 masses.
For instance, SRC1 is optimised for mt˜ = 225 GeV and mχ˜0
1 = 52 GeV, and SRC5 is optimised for
m˜t = 600 GeV and m
˜ χ0
1 = 427 GeV.
In addition, at least four jets must be assigned to the sparticle hemisphere of the event (NjS), and at least two of those jets must be b-tagged. Requirements on pISRT , the highest-pTb-tagged jet in the sparticle hemisphere
(pS,bT,1), and the fourth-highest-pTjet in the sparticle hemisphere (pST,4) are applied. To reject events with
poorly measured ETmiss, the difference in φ between the pmiss,trackT and pmissT , ∆φ pmiss T , p miss,track T , is required to be less than π/3 and the leading two jets are required to be separated in azimuthal angle from the pmissT : ∆φ pT,1−2, pmissT
> 0.4. The transverse mass of the sparticle system and pmiss
T , defined as mS,
is required to be greater than 400 GeV. The ISR system is also required to be separated in azimuthal angle from pmissT : ∆φ pISR T , p miss T
> 3.0. The selection criteria for SRC are summarised in Table3.
In addition to SRC1–5, a region optimised for discovery, SRC-Disc, is defined. In SRC-Disc, the same
requirements as in the other SRCs are applied, with the exception of requiring RISR> 0.5 and S > 11. As
Table 3: Selection criteria for SRC. The signal regions are separated into five categories based on ranges of RISR. Variable/SR SRC1 SRC2 SRC3 SRC4 SRC5 Trigger ETmiss Emiss T > 250 GeV N` exactly 0 Nj ≥ 4 pT,2 > 80 GeV pT,4 > 40 GeV Nb ≥ 2 Emiss,track T > 30 GeV ∆φ pmiss T , p miss,track T < π/3 ∆φ pT,1−2, pmiss T > 0.4 NS j ≥ 4 NS b ≥ 2 pISR T > 400 GeV pS,b T,1 > 50 GeV pS T,4 > 50 GeV mS > 400 GeV ∆φ pISR T , p miss T > 3.0 RISR 0.30–0.40 0.40–0.50 0.50–0.60 0.60–0.70 > 0.70
5.3 Signal regions D
SRD aims to select four-body top squark decays, for which the kinematic properties depend mainly on ∆m(˜t, ˜χ10). Four-body top squark decays result in final state particles with low pT, which are particularly
challenging to reconstruct. For instance, low-pTb-hadrons originating from such decays are usually not
contained in jets passing the minimum pT > 20 GeV requirement when ∆m(˜t, ˜χ
0
1) < 50 GeV, and therefore
cannot be tagged the same way as in SRA–C. To circumvent this problem and identify the low-pTb-hadrons
produced in a larger part of the four-body decay phase space, b-tagging using track-jets with pT > 5 GeV is
employed. Three signal region categories, SRD0, SRD1, and SRD2, are defined according to the b-tagged
jet multiplicity (zero, one, and two, respectively), and are optimised for ∆m(˜t, ˜χ10)= 20, 50, 80 GeV,
respectively. In SRD0 and SRD1 the presence of at least one b-tagged track-jet is required to recover undetected jets that contain b-hadrons.
An event including a pair of four-body top squark decays with ETmiss > 250 GeV is likely to be caused by
the presence of significant ISR emission. Thus the leading non-b-tagged jet, identified as the ISR jet (jISR),
is required to have large pT(p jISR
T ), as well as a large azimuthal separation
∆φ pjISR T , p miss T fromp miss T .
In order to reject events with mismeasured ETmiss originating from multijet and hadronic t ¯t decays,
requirements are made on ETmiss,trackand ∆φ pmiss T , p miss,track T
. Further background reduction is required in SRD0 and attained by selecting large
∆φmin pT,1−4, pmiss T
.
Only low-pTjets and track-jets (ptrackT,1 , pb,trackT,1 , pbT,1) are considered in all three categories. Requirements
are also made on b-tagged jet and track-jet pseudorapidities (|η1b,track|, |η1b|, |η2b|) to ensure they are in the central region of the detector, which make them more likely to originate from a top squark decay and
maximise the b-tagging performance. Only events with high ETmiss/
√
HTare kept, where HTis the scalar
sum of the transverse momenta of all jets. This kinematic variable was found to provide better signal
versus background discrimination than the object-based ETmisssignificance when the final state is composed
of low-pTobjects.
Given the absence of on-shell top quarks and W bosons, no top nor W reconstruction methods are used, such that additional discrimination of the signal from the background relies on differences in angular separation between jets and track-jets. In SRD1 (SRD2), requirements are made on the angular separation between the ISR jet and the b-tagged jet(s),
∆φ pjISR T , p b T,1 ( ∆φ pjISR T , p b T,1 and ∆φ pjISR T , p b T,2 ), to ensure the b-tagged jet(s) is (are) well-separated from the ISR jet. In SRD1, the minimum ∆φ between the leading four track-jets and the ISR jet (
∆φ pjtrack T,1−4, p jISR T
) is also required to be large, to separate the
low-pT top squark decay products from the ISR jet. Further background rejection is required in SRD0
and attained by requiring significant azimuthal separation between the leading b-tagged track-jet and the ISR jet (max
∆φ pjISR T , p btrack T
), and between the leadingb-tagged track-jet and the next track-jet most
likely to contain a b-hadron ( ∆φ pbtrack T,1 , p btrack T,2
). Table4summarises the full signal region selections for
Table 4: Signal region selections for SRD. Variables involving track-jets are denoted with the label ‘track’. A dash indicates that no selection is applied.
Variable/SR SRD0 SRD1 SRD2 Trigger ETmiss Emiss T > 250 GeV N` exactly 0 Nb exactly 0 exactly 1 ≥ 2 pjISR T > 250 GeV ∆φ pjISR T , p miss T > 2.4 Emiss,track T > 30 GeV ∆φ pmiss T , p miss,track T < π/3 Ntrack b ≥ 1 – ∆φmin pT,1−4, pmiss T > 0.4 – |ηb,track 1 | < 1.2 – max ∆φ pjISR T , p btrack T > 2.2 – ∆φ pbtrack T,1 , p btrack T,2 < 2.5 – pb,track T,1 < 50 GeV > 10 GeV – ptrack T,1 – < 40 GeV – ∆φ pjtrack T,1−4, p jISR T – > 1.2 – |ηb 1| – < 1.6 – ∆φ pjISR T , p b T,1 – > 2.2 |ηb 2| – < 1.2 pb T,1 – < 175 GeV ∆φ pjISR T , p b T,2 – > 1.6 Emiss T / √ HT > 26√GeV > 22√GeV
6 Background estimation
The main SM background process in SRA, SRB, and SRD is Z → ν ¯ν production in association with
heavy-flavour jets. In SRC, t ¯t production dominates, including mostly events where one W boson decays hadronically and the other W boson decays via a τ-lepton and its corresponding neutrino (W + jets). Other important background processes include leptonic W decays produced in association with heavy-flavour jets, a single top quark produced with a W boson, and the irreducible background from t ¯t + Z , where the Z boson decays into two neutrinos.
Significant background contributions are estimated primarily from comparisons between data and simulation in specially designed ‘control regions’ (CRs), which have a selection orthogonal to all SRs and aim to enhance a particular background process, while probing a similar event topology. Sufficient data are needed to minimise the statistical uncertainties in the background estimates in the CRs, while the extrapolation from the CR to the SR, evaluated with simulated events, should be as small as possible to reduce the associated systematic uncertainties. Furthermore, CR selection criteria are chosen to minimise potential contamination by signal. The signal contamination is below 10% in all CRs for top squark and neutralino mass combinations that have not yet been excluded at 95% confidence level by previous ATLAS searches [22–25,27,28].
Separate CRs are defined for SRA–B, SRC and SRD, with the observed number of events in each region
included in one of the three dedicated binned profile likelihood fits [120] of the analysis (SRA–B fit, SRC
fit, SRD fit). The CRs are defined so that all CRs associated with a given signal region are orthogonal to the other CRs for that specified region. Partial overlaps remain possible between regions included in different fits. Each likelihood function is built as the product of Poisson probability density functions, describing the observed and expected numbers of events in the control regions. Additional terms, constrained by Gaussian probability density functions accounting for MC statistics and common systematic uncertainties (discussed
in Section7) between the control and signal regions and their correlations, are included and treated as
nuisance parameters in the fitting procedure.
Control regions targeting the Z + jets, t ¯t, W + jets, single-top and t ¯t + Z backgrounds are included in the SRA–B fit, while for the SRC fit only a t ¯t control region is defined. For the SRD fit, control regions are defined for Z + jets, t ¯t, and W + jets backgrounds. For each fit (SRA–B, SRC, and SRD), the normalisations of these backgrounds are determined simultaneously in order to best match the observed data in each control region, including contributions from all backgrounds (background-only fit). No observed or expected number of events in the signal regions is considered at this stage. In cases where there are multiple control regions for one background in one fit, the fit yields one normalisation which best fits all regions.
Contributions from all-hadronic t ¯t and multijet production are found to be negligible in all signal regions except for SRC, where they are subdominant. These backgrounds are estimated from data collected by
single-jet triggers using a jet smearing procedure described in Ref. [121] and are fixed in the fit, with
an uncertainty assigned to them (discussed in Section7). The contributions from all other background
processes (diboson, t Z , t ¯tH, t ¯tW , tW Z ) are less than 15% of the total SM background expectations and are fixed at the value expected from the simulation, using the most accurate theoretical cross sections available, while their uncertainties are included as additional nuisance parameters in the fit. In the following, the multijet, diboson, t Z , t ¯tH, t ¯tW , and tW Z backgrounds are grouped together and referred to as ‘other’. Validation regions (VRs) are defined for the major sources of background in each signal region such that they are orthogonal to the control regions and the signal regions. They usually suffer from a higher signal contamination (up to 20%) than the CRs, but probe a kinematic region which is closer to that of
the SRs. The background normalisation factors from the simultaneous fit are applied to their respective backgrounds and compared with data in each VR to verify good agreement and that the simultaneous fit is well-behaved.
Detailed CR definitions for the estimation of Z + jets (CRZ), t ¯t + Z (CRTTZ), t ¯t (CRT), W + jets (CRW), and single-top (CRST) backgrounds are described in the following subsections, while a summary of the
control region strategy in the SRA–B and SRD fits is shown in Figure3. The strategy for SRC only involves
one control region (extrapolating from an electron or muon multiplicity of zero in the SR to an electron or muon multiplicity of one in the CR) and one validation region (extrapolating over
∆φ pISR T , p miss T ) for the dominant t ¯t background. N Nb 0 1 2 3 1 2
SR
T
ST
W
Z
TTZ
+
VR
(a) N Δ R( b , ) 0 1 2 3 1T
W
Z
SR
VR
+
Y1 Y2 (b)Figure 3: A summary of the background control region strategy used in the (a) SRA–B and (b) SRD fits. The orthogonality between the Z + jets (Z), t ¯t + Z (TTZ), t ¯t (T), W + jets (W), and single-top (ST) backgrounds’ control regions and the signal and validation regions (SR+VR) included in the SRA–B fit rely on the number of leptons, N`, and the number of b-tagged jets, Nb. T and ST are made orthogonal by selecting either low-pT(< 20 GeV)
or high-pT(> 27 GeV) leptons, respectively. The orthogonality between the Z + jets (Z), t ¯t (T), and W + jets
(W) backgrounds’ control regions and the signal and validation regions (SR+VR) included in the SRD fit relies on N`and, for N` = 1, the angular distance between the lepton and the closest b-tagged jet (b-tagged track-jet in
CRWD0), ∆R(b, `). Placeholders for the values of ∆R(b, `) are shown as Y1and Y2and vary in different SRD regions
depending on Nb. Additional selections not appearing on the sketches ensure orthogonality between the SR and the VR. Additional extrapolations from CRs to SRs in other kinematic quantities not necessarily shown in this sketch are region-specific and detailed in the text.
6.1 Z+ jets background estimation
The normalisation of the simulation of Z → ν ¯ν produced in association with heavy-flavour jets is estimated
from Z → e+e−and Z → µ+µ−events produced in association with heavy-flavour jets, which is the strategy
adopted for SRA–B (CRZAB) and SRD (CRZD). Data events passing a single-electron or single-muon trigger are considered, and events with two control electrons or two control muons with opposite charge
are selected. In CRZAB (CRZD), p`T > 27, 20 GeV (p`T > 30, 20 GeV) is required for the leading and
subleading leptons, respectively, which must also have an invariant mass within 10 GeV of the Z boson
mass, mZ= 91 GeV. Events with ETmiss > 50 GeV (ETmiss > 70 GeV) in CRZAB (CRZD) are discarded
added to the pmissT to mimic the Z (→ ν ¯ν) + jets decays in the SRs, forming the quantity Emiss 0
T . High-pT Z
bosons are then effectively selected by requiring large Emiss
0
T .
Recalculated quantities that use Emiss 0
T instead of E
miss
T are identified by the addition of a prime (e.g. m
b,min0
T ).
Where possible, the CR selection criteria are identical to the criteria used in the signal region; however, the
criteria for key variables such as mb,min
0
T and S
0
for CRZAB, or Emiss
0
T /
√
HT for CRZD, are loosened to
enhance the number of data events in the CR. The Z + jets CR included in the SRA–B (SRD) fit is split
into two (three) categories depending on m2R=1.2(Nb), to minimise the extrapolation across the various SR
categories. There are only two categories in CRZAB, CRZAB-TTTW (representing the background in the TT and TW signal categories) and CRZAB-T0, due to the limited number of data events. The detailed set
of selection criteria for the Z + jets CRs are presented in Table5; representative distributions for CRZ
variables that have looser requirements than in the SRs are shown in Figure4.
10 15 20 25 30 S′ 5 10 15 20 25 Events / 1 Z+jets ttZ Other SM Total Data ATLAS -1 = 13 TeV, 139 fb s CRZAB-TTTW (a) 200 250 300 350 400 450 500 550 600 650 700 [GeV] 2 χ T2, m 5 10 15 20 25 30 35 Events / 25 GeV Z+jets ttZ Other SM Total Data ATLAS -1 = 13 TeV, 139 fb s CRZAB-TTTW (b) 0.5 1 1.5 2 2.5 3 3.5 4 ) 2 , b 1 ( b R ∆ 10 20 30 40 50 60 Events / 0.2 Z+jets ttZ Other SM Total Data ATLAS -1 = 13 TeV, 139 fb s CRZAB-T0 (c) 10 12 14 16 18 20 22 24 26 28 30 ] 1/2 [GeV T H / miss’ T E 10 20 30 40 50 60 70 1/2 Events / 2 GeV Z+jets Other SM Total Data ATLAS -1 = 13 TeV, 139 fb s CRZD0 (d)
Figure 4: Distributions illustrating the level of agreement between data (points) and the SM expectation (stacked histograms, after simultaneously fitting to all backgrounds) in several Z + jets control regions: (a) S0and (b) mT2, χ2
for CRZAB-TTTW, (c) ∆R (b1, b2) for CRZAB-T0, and (d) Emiss
0
T /
√
HTfor CRZD0. The hatched uncertainty band around the SM expectation includes the combination of MC statistical, theory-related and detector-related systematic uncertainties. The rightmost bin in each plot includes all overflows.
Table 5: Selection criteria for the Z + jets control regions. The defining extrapolation for these control regions is over the number of leptons; two electrons or muons (`) from Z decays are required, compared with zero leptons in the signal regions. A dash indicates that no selection is applied. Variables for which the signal and control region requirements differ are highlighted by a thick border around the cell that contains the requirement. Requirements are made on the following variables in the signal regions but have no equivalent requirement in the control regions: τ-veto, mR=0.8 1 , j R=1.2 1 (b), j R=1.2 2 (b), ∆R (b1, b2), m b,max T , mT2, χ2, Emiss,track T , and ∆φ pmiss T , p miss,track T .
Variable/CR CRZAB-TTTW CRZAB-T0 CRZD0 CRZD1 CRZD2
Trigger single electron or muon
Control ` exactly 2, same flavour / opposite sign
Additional baseline ` 0 m(`, `) 81–101 GeV Emiss T < 50 GeV < 70 GeV p` T > 27, > 20 GeV > 30, > 20 GeV Emiss0
T > 200 GeV > 250 GeV > 150 GeV > 200 GeV
Nj ≥ 4 – pT, 2 > 80 GeV – pT, 4 > 40 GeV – Nb ≥ 2 exactly 0 exactly 1 ≥ 2 m1R=1.2 > 80 GeV – mR=1.2 2 > 60 GeV < 60 GeV – mTb,min0 > 150 GeV – S0 > 10 – pjISR
T – > 250 GeV > 200 GeV > 250 GeV
∆φ pjISR T , p miss T – > 2.4 Ntrack b – ≥ 1 – ∆φmin pT, 1−4, pmissT – > 0.4 – |ηb,track 1 | – < 1.2 – max ∆φ pjISR T , p btrack T – > 2.2 – ∆φ pbtrack T, 1 , p btrack T, 2 – < 2.5 – pb,track T, 1 – < 50 GeV > 10 GeV – ptrack T, 1 – < 40 GeV – ∆φ pjtrack T, 1−4, p jISR T – > 1.2 – |ηb 1| – < 1.6 – ∆φ pjISR T , p b T, 1 – > 1.8 > 2.2 |ηb 2| – < 1.2 pb T, 1 – < 175 GeV ∆φ pjISR T , p b T, 2 – > 1.6 Emiss0 T / √ HT – > 12 √ GeV > 8 √ GeV
6.2 t ¯t+ Z background estimation
The SM production of t ¯t + Z , where Z → ν ¯ν, is a significant source of background in SRA and SRB and
is largely irreducible. To estimate this background, a three-lepton (electrons and muons) region is defined, to maximise the purity of t ¯t + Z .
Events that pass a single-electron or single-muon trigger are selected. The trigger electron or muon
must pass the requirements for a control electron or muon and have offline pT > 27 GeV. Exactly two
additional control leptons (electrons or muons) with pT > 20 GeV are required. The sum of the charges
of the three leptons is required to equal 1 or −1, while two of the leptons are required to have the same flavour and opposite charge. The pair of same-flavour, opposite-sign leptons that is most consistent with the Z boson mass forms the Z boson candidate and is required to have an invariant mass satisfying
81 GeV < m(`, `) < 101 GeV. The Z boson candidate is required to have pT > 200 GeV. The remaining
lepton and the pmissT are treated as non-b-tagged jets in the computation of all jet-related variables (such as
pT), to mimic hadronic W decays.
Four jets are required to be in the event, in addition to the lepton not associated with the Z boson candidate and the pmissT , and two of the jets are required to be b-tagged jets. The selection criteria are summarised in
Table6. Representative distributions for CRTTZ variables that have looser requirements than in the SRs
are shown in Figure5.
0 2 4 6 8 10 12 14 16 S 2 4 6 8 10 12 14 16 18 20 22 Events / 1 Z t t Other Z+jets SM Total Data ATLAS -1 = 13 TeV, 139 fb s CRTTZ (a) 200 300 400 500 600 700 800 pT(ℓ, ℓ)[GeV] 5 10 15 20 25 30 35 Events / 50 GeV Z t t Other Z+jets SM Total Data ATLAS -1 = 13 TeV, 139 fb s CRTTZ (b)
Figure 5: Distributions illustrating the level of agreement between data (points) and the SM expectation (stacked histograms, after simultaneously fitting to all backgrounds) in the t ¯t + Z control region: (a) S and (b) pT(`, `)
for CRTTZ. The hatched uncertainty band around the SM expectation includes the combination of MC statistical, theory-related and detector-related systematic uncertainties. The rightmost bin in each plot includes all overflows.
Table 6: Selection criteria for the t ¯t + Z control region. The defining extrapolation for these control regions is over the number of leptons; three leptons (a combination of electrons and muons) from W and Z decays is required, compared with zero leptons in the signal region. Variables for which the signal and control region requirements differ are highlighted by a thick border around the cell that contains the requirement. Requirements are made on the following variables in SRA and SRB but have no equivalent requirement in the control region: ∆φmin pT,1−4, pmissT
, mb,min T , τ-veto, m R=1.2 1 , m R=1.2 2 , m R=0.8 1 , j R=1.2 1 (b), j R=1.2 2 (b), ∆R (b1, b2), m b,max T , S, and mT2, χ2. Variable/CR CRTTZ
Trigger single electron or muon
Control ` exactly 3
Additional baseline ` 0
Sum of muon and electron charges +1 or −1
` associated with Z exactly 2, same flavour / opposite sign
m(`, `) 81–101 GeV p` T > 27, > 20, > 20 GeV pT(`, `) > 200 GeV Nj ≥ 4 Nb ≥ 2
pT,2 (including ETmissand non-Z `) > 80 GeV
pT,4 (including ETmissand non-Z `) > 40 GeV
6.3 t ¯t, W + jets, and single-top background estimation
The t ¯t background in SRB, SRC, and SRD originates from events where a W boson decays into a hadronically decaying τ-lepton, where the τ-lepton is either not reconstructed (due to falling below the jet
pTthreshold of 20 GeV), or is reconstructed as a jet. In order to model this process in the CRs, events that
pass the same ETmisstrigger as the signal region, but also have a control electron or muon, are selected. The electron or muon is used as a proxy for the τ-lepton in the SRs.
In SRA and SRB, the hadronically decaying τ-leptons are most likely to have fallen below the jet
pT > 20 GeV requirement, such that for the t¯t and W + jets control regions (CRTAB and CRWAB,
respectively), exactly one control electron in the range 4.5 < pTe < 20 GeV or muon in the range
4.0 < pTµ < 20 GeV is required. In SRC and SRD, the hadronically decaying τ-leptons have higher pT,
such that one control electron or muon with pT > 20 GeV is required, and is treated as a non-b-tagged jet
in the computation of all jet-related variables.
In the t ¯t control regions (CRTC, CRTD), the angular separation between the electron or muon and the b-tagged jet closest to the electron or muon, ∆R(b, `), is used to enhance the t ¯t purity. In CRTD, ∆R(b, `) is also used to ensure orthogonality with the W + jets control region (CRWD). All t ¯t control regions (CRTAB,
CRTC, CRTD) have an upper bound on mT `, pmissT
signal regions of other ATLAS ongoing studies in the one-lepton plus missing transverse momentum channel, as well as to reduce potential signal contamination. In addition to the variables used in SRC,
CRTC has a mV/mS < 0.75 requirement, where mSis the variable used in SRC and mVis the invariant
mass of all visible objects, which provides additional signal rejection. The t ¯t CR included in the SRD fit is split into two categories (CRTD1 or CRTD2, which require exactly one or at least two b-tagged jets, respectively) to minimise the extrapolation across the various SR categories. The various t ¯t control regions
designed for the analysis are defined in Table7. Representative distributions are shown in Figure6.
0 100 200 300 400 500 600 700 800 900 1000 [GeV] ,max b T m 10 20 30 40 50 60 70 Events / 50 GeV t t Single top W+jets Other SM Total Data ATLAS -1 = 13 TeV, 139 fb s CRTAB (a) 0.3 0.4 0.5 0.6 0.7 0.8 0.9 ISR R 5 10 15 20 25 30 35 40 45 Events / 0.1 t t Single top W+jets Other SM Total Data ATLAS -1 = 13 TeV, 139 fb s CRTC (b) 10 15 20 25 30 ] 1/2 [GeV T H / miss T E 10 20 30 40 50 1/2 Events / 2 GeV t t W+jets
Single top SM Total Data ATLAS -1 = 13 TeV, 139 fb s CRTD1 (c) 14 16 18 20 22 24 ] 1/2 [GeV T H / miss T E 10 20 30 40 50 1/2 Events / 0.5 GeV t t W+jets
Single top Other SM Total Data ATLAS -1 = 13 TeV, 139 fb s CRTD2 (d)
Figure 6: Distributions illustrating the level of agreement between data (points) and the SM expectation (stacked histograms, after simultaneously fitting to all backgrounds) in the t ¯t control regions: (a) mTb,maxfor CRTAB, (b) RISR
for CRTC, and ETmiss/ √
HTfor (c) CRTD1 and (d) CRTD2. The hatched uncertainty band around the SM expectation includes the combination of MC statistical, theory-related and detector-related systematic uncertainties. The rightmost bin in each plot includes all overflows.
The W + jets background is important for SRA–B and SRD, while the single-top background is significant for SRA–B only; corresponding control regions (CRWAB, CRWD, and CRSTAB, respectively) are defined
in Table8. The W + jets background in SRA–B originates from W boson decays into low-pTτ-leptons;
Table 7: Selection criteria for the t ¯t control regions. The defining extrapolation for these control regions is over the number of leptons; one electron or muon (`) from W decays is required, compared with zero leptons in the signal region. A dash indicates that no selection is applied. Variables for which the signal and control region requirements differ are highlighted by a thick border around the cell that contains the requirement. Requirements are made on the following variables in the signal regions but have no equivalent requirement in the control regions: RISR, τ-veto,
mR=0.8 1 , j R=1.2 1 (b), j R=1.2 2 (b), m b,max T , mT2, χ2. Variable/CR CRTAB CRTC CRTD1 CRTD2 Trigger Emiss T Emiss T > 250GeV Control` exactly1 Additional baseline` 0 p` T 4.5 (4.0) < p e (µ) T < 20GeV pT> 20GeV mT`, pmiss T
< 120GeV < 100GeV < 120GeV
Nj ≥ 4 ≥ 3 – pT, 2 > 80GeV – pT, 4 > 40GeV – Nb ≥ 2 exactly 1 ≥ 2 ∆φmin pT, 1−4, pmiss T > 0.4 – mR=1.2 1 > 120GeV – mb,min T > 150GeV – ∆R (b1, b2) > 1.4 – S > 14 > 5 – ∆φ pT, 1−2, pmiss T – > 0.2 – NS j – ≥ 4 – NS b – ≥ 2 – pISR T – > 400GeV – pS, b T, 1 – > 40 GeV – pS T, 4 – > 50GeV – mS – > 400 GeV – ∆φ pISR T , pmissT – > 3.0 – mV /mS – < 0.75 – ∆R(b, `) – < 2.0 < 1.8 Emiss, track T – > 30GeV ∆φ pmiss T , p miss, track T – < π/3 pjISR T – > 250GeV ∆φ pjISR T , p miss T – > 2.4 ∆φ pjISR T , p b T, 1 – > 2.2 Ntrack b – ≥ 1 – pb,track T, 1 – > 10GeV – ptrack T, 1 – < 40GeV – ∆φ pjtrack T, 1−4, p jISR T – > 1.2 – |ηb 1| – < 1.6 – Emiss T / √ HT – > 8 √ GeV > 14 √ GeV |ηb 2| – < 1.2 pb T, 1 – < 175GeV ∆φ pjISR, pb – > 1.6
which makes CRWAB orthogonal to CRTAB. The single-top control region, CRSTAB, is defined as having
exactly one control electron or muon with pT > 20 GeV (making CRSTAB orthogonal to both CRWAB
and CRTAB) and two or more b-tagged jets. A requirement of pT > 20 GeV is used in CRWD because the
W+ jets background in SRD is dominated by high-pTelectrons, muons, and τ-leptons. To enhance the
purity of the W + jets background in CRWD and ensure orthogonality with CRTD, lower bounds are put on ∆R(b, `), which is defined with respect to the b-tagged jet (b-tagged track-jet) closest to the lepton in CRWD1–2 (CRWD0). Representative distributions for the various W + jets and single-top control regions
defined in the analysis are shown in Figure7.
200 250 300 350 400 450 500 550 600 650 700 [GeV] 2 χ T2, m 10 20 30 40 50 60 Events / 25 GeV W+jets tt Single top Other SM Total Data ATLAS -1 = 13 TeV, 139 fb s CRWAB (a) 14 16 18 20 22 24 26 ] 1/2 [GeV T H / miss T E 10 20 30 40 50 1/2 Events / 1 GeV W+jets tt Single top SM Total Data ATLAS -1 = 13 TeV, 139 fb s CRWD0 (b) 8 10 12 14 16 18 20 ] 1/2 [GeV T H / miss T E 10 20 30 40 50 1/2 Events / 1 GeV W+jets tt Single top SM Total Data ATLAS -1 = 13 TeV, 139 fb s CRWD1 (c) 200 400 600 800 1000 [GeV] ,max b T m 5 10 15 20 25 30 Events / 50 GeV Single top tt W+jets Other SM Total Data ATLAS -1 = 13 TeV, 139 fb s CRSTAB (d)
Figure 7: Distributions illustrating the level of agreement between data (points) and the SM expectation (stacked histograms, after simultaneously fitting to all backgrounds) in several W + jets and single-top control regions: (a) mT2, χ2for CRWAB, Emiss
T /
√
HTfor (b) CRWD0 and (c) CRWD1, and (d) mb,max
T for CRSTAB. The hatched uncertainty
band around the SM expectation includes the combination of MC statistical, theory-related and detector-related systematic uncertainties. The rightmost bin in each plot includes all overflows.
Table 8: Selection criteria for the W + jets and single-top control regions. The defining extrapolation for these control regions is over the number of leptons; one electron or muon (`) from W decays is required compared with zero leptons in the signal regions. A dash indicates that no selection is applied. Variables for which the signal and control region requirements differ are highlighted by a thick border around the cell that contains the requirement. Requirements are made on the following variables in the signal regions but have no equivalent requirement in the control regions: mR=1.2 2 , m R=0.8 1 , j R=1.2 1 (b), j R=1.2 2 (b), m b,max T , mT2, χ2.
Variable/CR CRSTAB CRWAB CRWD0 CRWD1 CRWD2
Trigger ETmiss Emiss T > 250 GeV Control ` exactly 1 Additional baseline ` 0 p` T pT> 20 GeV 4.5 (4.0) < p e (µ) T < 20 GeV pT> 20 GeV mT`, pmissT
< 100 GeV < 120 GeV < 100 GeV
Nj ≥ 4 –
pT, 2 > 80 GeV –
pT, 4 > 40 GeV –
Nb ≥ 2 exactly 1 exactly 0 exactly 1 ≥ 2
∆φmin pT, 1−4, pmiss T > 0.4 – mR=1.2 1 > 120 GeV < 60 GeV – mTb,min > 200 GeV – ∆R (b1, b2) > 1.4 – – < 1.0 mb, ` min > 100 GeV – τ-veto yes – – S > 14 – ∆R(b, `) – > 2.0 > 1.6 > 1.8 > 2.2 pTjISR – > 250 GeV Emiss, track T – > 30 GeV ∆φ pmiss T , p miss, track T – < π/3 ∆φ pjISR T , p miss T – > 2.4 Ntrack b – ≥ 1 – |ηb,track 1 | – < 1.2 – max ∆φ pjISR T , p btrack T – > 2.2 – ∆φ pbtrack T, 1 , p btrack T, 2 – < 2.5 – pb,track T, 1 – < 50 GeV > 10 GeV – ptrack T, 1 – < 40 GeV – ∆φ pjtrack T, 1−4, p jISR T – > 1.2 – |ηb 1| – < 1.6 – pb T, 1 – < 175 GeV |ηb 2| – < 1.2 Emiss T / √ HT – > 14 √ GeV > 8 √ GeV > 12 √ GeV
CRTABCRSTABCRWABCRZAB-TTTWCRZAB-T0CRTTZCRTC CRTD1CRTD2CRWD0CRWD1CRWD2CRZD0CRZD1CRZD2 0.5 1 1.5 bkg µ Post-fit 50 100 150 200 250 300 350 400 450 Events tt Z+jets
W+jets Single top Z t t Other SM Total Data ATLAS -1 = 13 TeV, 139 fb s Pre-fit ATLAS -1 = 13 TeV, 139 fb s Pre-fit
Figure 8: A summary of the normalisation factors determined from the various background-only fits. The total number of data events (points) and the SM expectation (stacked histograms) are shown in each control region before the fit. The uncertainty associated with the SM expectation includes the combination of MC statistical uncertainties, theory-related and detector-related systematic uncertainties. The normalisation factor applied to each background source (µbkg) after the fit and respective uncertainty, including the combination of MC statistical uncertainties,
theory-related and detector-related systematic uncertainties, is shown in the lower panel. The control regions included in the SRA–B, SRC and SRD fits are separated by vertical dashed lines.
6.4 Validation of background estimates
The background normalisation factors derived from the SRA–B, SRC and SRD background-only fits are
summarised in Figure8. Most normalisation factors are within 1σ of unity, where σ denotes the total
uncertainty, including the data statistical uncertainty in the CRs and the theory-related and detector-related
systematic uncertainties (described in Section7). However, the t ¯t (t ¯t and Z + jets) normalisation factors
derived from the SRC (SRD) fit are lower than unity by one to two σ. Significant amounts of ISR radiation are required in SRC, SRD, and the associated control regions, unlike SRA–B and the associated control regions. The simulated event yields in t ¯t-enriched regions compare differently with data in SRA–B control regions and SRC–D control regions, overestimating the number of events in the latter, while fairly good agreement is observed in the former. A similar effect is observed in CRZAB and CRZD. These observations point to a mismodelling possibly related to the ISR system in t ¯t and Z + jets events. The fitting procedure corrects for this mismodelling and is validated in the VRs discussed below.
Validation regions are defined to check the validity of the normalisation factors in the signal regions and to check the ability of the MC to describe the shapes of the kinematic variables over which extrapolations are made in propagating background estimates from the control regions to the signal regions. The defining extrapolation from control to signal regions is in the lepton multiplicity, whereas the validation regions include only events with zero leptons, as in the signal regions. Validation regions are designed for the
Z + jets background in SRA (VRZA) and SRB (VRZB-TTTW, VRZB-T0) and SRD (VRZD0–2), as well
as for the t ¯t background in SRA–B (VRTAB), SRC (VRTC), and SRD (VRTD1–2). Requirements applied in the SRs are modified in the VRs to ensure orthogonality with the SRs, to limit signal contamination, and
